An implication system (IS) Σ on a finite set S is a set of rules called Σ-implications of the kind A→Σ B, with A,B⊆ S. A subset X ⊆ S satisfies A→Σ B when “A⊆ X implies B⊆ X” holds, so ISs can be used to describe constraints on sets of elements, such as dependency or causality. ISs are formally closely linked to the well known notions of closure operators and Moore families. This paper focuses ...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

Abstract When an algebraic logic based on a poset instead of lattice is investigated then there natural problem how to introduce implication be everywhere defined and satisfying (left) adjointness with conjunction. We have already studied this for the quantum mechanics which orthomodular or effects so-called effect algebra only partial need not lattice-ordered. For this, we introduced operator ...

Classical logic is unfortunately defective with its problematic definition of implication relation, the “material implication”. This work presents a corrected definition of implication relation to replace material implication in classical logic. Common “paradoxes” of material implication are avoided while simplicity and usefulness of the system are reserved with this definition of implication r...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Although various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints not studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear extension of logic with implication, extend it Dynamic (DLTQL). This has operators express transitions by unitary (quantum gates) ones those projections (projective measurement)....